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scalingfunctions

DWT filter bank time-domain scaling functions

Description

phi = scalingfunctions(fb) returns the time-centered scaling functions for each level of the discrete wavelet transform (DWT) filter bank fb.

example

[phi,t] = scalingfunctions(fb) returns the sampling instants, t.

Examples

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Create a seven-level DWT filter bank for a length 2048 signal, using the Daubechies db2 wavelet and a sampling frequency of 1 kHz.

wv = "db2";
len = 2048;
Fs = 1e3;
lev = 7;
fb = dwtfilterbank('SignalLength',len,'Wavelet',wv,'Level',lev,'SamplingFrequency',Fs);

Plot the scaling functions for each level of the filter bank.

[phi,t] = scalingfunctions(fb);
plot(t,phi')
grid on
xlim([-len/2*1e-3 len/2*1e-3])
title('Scaling Functions')
legend('A1','A2','A3','A4','A5','A6','A7')

Figure contains an axes object. The axes object with title Scaling Functions contains 7 objects of type line. These objects represent A1, A2, A3, A4, A5, A6, A7.

Input Arguments

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Discrete wavelet transform (DWT) filter bank, specified as a dwtfilterbank object.

Output Arguments

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Time-centered scaling functions of the filter bank fb, returned as a real-valued L-by-N matrix, where L is the filter bank Level and N is the SignalLength. The scaling functions are ordered in phi from the finest scale resolution to the coarsest scale resolution.

Sampling instants, returned as a real-valued vector t of length N, where N is the filter bank SignalLength. Sampling instants lie in the interval [½NDT,½NDT), where DT is the filter bank sampling period (reciprocal of the filter bank sampling frequency).

Introduced in R2018a